1. **Simplify the algebraic expression:** Given expression: $-3 - x^2 - 6x - 5x^2 + 3x - 1$ 2. **Combine like terms:** - Combine $x^2$ terms: $-x^2 - 5x^2 = -6x^2$ - Combine $x$ terms: $-6x + 3x = -3x$ - Combine constants: $-3 - 1 = -4$ 3. **Write the simplified expression:** $$-6x^2 - 3x - 4$$ --- 4. **Evaluate the arithmetic expression:** $$5 \times \frac{2}{10} + \left(-\frac{3}{6}\right) - 6$$ 5. **Calculate each term:** - $5 \times \frac{2}{10} = 1$ - $-\frac{3}{6} = -0.5$ 6. **Sum the values:** $$1 - 0.5 - 6 = -5.5$$ --- 7. **Multiply fractions:** $$\frac{12}{21} \cdot 3$$ 8. **Simplify:** $$\frac{12}{21} \cdot 3 = \frac{12 \times 3}{21} = \frac{36}{21} = \frac{12}{7} \approx 1.714$$ --- 9. **Find the area of the rectangle:** - Rectangle sides: 7 ft and 7 ft - Area formula: $\text{Area} = \text{length} \times \text{width}$ 10. **Calculate area:** $$7 \times 7 = 49 \text{ ft}^2$$ --- **Final answers:** - Simplified expression: $-6x^2 - 3x - 4$ - Arithmetic evaluation: $-5.5$ - Fraction multiplication: $\frac{12}{7} \approx 1.714$ - Rectangle area: $49$ ft$^2$